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Lecture
3: The Night Sky - II
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| Astronomy
101/103 |
Terry
Herter, Cornell University
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Lecture
Topics
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- The
changing sky (continued)
- Using
RA and Dec to find objects
- In-class
planetarium demonstration
- Magnitudes
- Fluxes
and magnitudes
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Equatorial
Coords
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Astronomers
use equatorial coordinates to locate objects on the celestial
sphere.
Right
Ascension (RA or a)
- Equivalent
to longitude
- RA
is measured in hours
- The
range is from 0 to 24 hours increasing on sky towards
the east.
- The
"zero point" is towards the constellation Pices.
Declination
(Dec or d)
- Equivalent
to latitude
- Dec
is measured in degrees.
- The
zero is on the equator
- North
Pole = 90 deg. , South Pole = -90 deg.
Notes:
- The
equatorial (celestial) coordinate system is fixed on the
sky.
- The
coordinates of the stars and constellations do not change
(ignoring precession).
- Since
it is an "earth-centered" system the coordinates of the
sun do change.
The
diagram below illustrates the definition of RA along the
equatorial plane and show the ecliptic plane and north celestial
pole.
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Equatorial
and
Ecliptic
Planes
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The
diagram below illustrates the definition of RA along the
equatorial plane and show the ecliptic plane and north celestial
pole.
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Equinoxes
and the
Seasons
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Definitions
and the Seasons
The
ecliptic intersects the equatorial plane at two locations,
the vernal equinox (0 hr RA) and autumnal equinox
(12 hr RA).
As
the earth moves around the sun, the sun changes position
in the sky relative to the background stars. Thus the RA
of the sun changes every day.
For instance, on the first day of spring the sun is at the
location of the vernal equinox, RA = 0 hr. On the first
day of fall the sun appears in the direction of the autumnal
equinox, RA = 12 hr.
The
table below summarizes the location of the sun at the beginning
of each season.
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Event
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Sun's
RA
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Comment
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first
day of spring
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0
hr
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Vernal
Equinox
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summer
solstice
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6
hr
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first
day of fall
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12
hr
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Autumnal
equinox
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winter
solstice
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18
hr
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The
Fall
Sky
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The
figure below shows the location of the earth relative
to the sun on the first day of fall. At local midnight
an observer (for instance, you!) is standing on the opposite
side of the earth from the sun and RA = 0 hr is crossing
the meridian. Looking to the eastern horizon you see RA
= 6 hr while looking to the western horizon you see RA
= 18 hr.
RA
= 0 hr on the meridian at midnight on Sep. 21.
The
arrows indicate the direction of the celestial sphere
of RA = 0, 6, 12, and 18 hr. Note that the earth is not
located at RA = 0 hr in this diagram. The equatorial coordinate
system is centered on the earth, so the RA and Dec of
the earth have no meaning.
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The
Revolving
Earth
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Revolving Earth and the Changing Sky
Since
the earth revolves around the sun, at the same time
each night, a different RA will be on the meridian at different
times of the year.
For
instance at midnight for the following dates, the RA's on
the meridian are:
- Sep.
21 ===> 0 hr
- Dec.
21 ===> 6 hr
- Mar.
21 ===> 12 hr
- June
21 ===> 18 hr
The
two figures below show "snapshots" of the sun-earth
system on the first day of winter and spring.
RA
= 6 hr on the meridian at midnight on Dec. 21.
RA
= 12 hr on the meridian at midnight on Mar. 21.
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The
Rotating
Earth
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The
Rotating Earth and the Changing Sky
As
the earth rotates on its axis, the stars move through
the sky over the course of a night. Like the sun, planets,
and the moon, the stars rise in the east and set in the
west due to the earth's rotation.
Consider the case illustrated below. At midnight, RA = 0
hr is on the meridian. As the earth turns, the observer
moves. The graphic illustrates the location of the observer
at 4:00 AM. Now RA = 4 hr is on the meridian and RA = 0
hr will appear west of the meridian to the observer.
On
the first day of fall (Sep. 21), RA = 0 hr on the meridian
at midnight. At 4:00 AM, RA = 4 hr will been on the meridian.
Six
months later on the first day of sping (Mar. 21), RA = 12
hr is on the meridian at midnight. At 4:00 AM, RA = 16 hr
will been on the meridian.
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Summary
of the
Changing
Sky
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The
figure below gives an overview of the different parts of
the sky you can view different times of the year.
All
observers (people) are shown at local midnight, except for
the fall where observers are shown at midnight, 4:00 AM,
and noon.
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Movement
of the
Sky
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Your
general knowledge tells you that objects (sun, moon, stars,
etc.) rise in the east, cross the meriadian overhead, and
set in the west.
Due
to the revolution of the earth about the sun, these events
happen earlier each successive night. Thus
- Each
night a given object will pass over the meridian
4 minutes earlier.
- This
corresponds to 2 hours earlier each month, or 24 hours
in one year.
- Objects
rise and set earlier each day.
At
a given time, the RA crossing the meridian increases
by 4 min. per day.
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Example
1: motion over the night
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Suppose
you see a star on the meridian at midnight.
As you watch it, it moves to the west. So
if you went out at 3:00 AM you would find
the star west of the meridian. Likewise, if
you had gone out earlier you would find the
star east of the meridian.
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Example
2: motion over several months
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Suppose
you observe a star on the meridian tonight
at midnight. One month from now you go out
to look at the sky at the same time. The star
would now appear in the west. In fact, it
would be "2 hours over" to the west.
(Note that the sky at 2:00 AM tonight will
be the same as the sky at midnight one month
from now!)
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Rotation
of the
Earth
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RA
= 0 hr on the meridian at midnight on Sep. 21. At 4:00 AM,
RA = 4 hr will be on the meridian. As illustrated in the
figure below this change is produced by the rotation of
the earth.
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Revolution
of the
Earth
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As
illustrated below, when the earth has revolve around the
sun by 180 degrees (6 months). There is a new view of the
sky. RA = 12hr on the meridian at midnight on Sep. 21. At
4:00 AM, RA = 16 hr will be on the meridian.
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Finding
an
Object
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You
can either know when the constellation an object is in is
up or you can use the RA of the object to figure out when
it is up. The first figure below illustrates the constellation
approach while the second figure illustrates the RA approach.
Memorizing
constellations and their availability is one way to tell
when an object is visible.
Learning
how to use an objects RA to determine visibility makes
things much easier. (Although maybe not as much fun.)
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Finding
Orion
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what date is Orion on the meridian at midnight? At 3:00 AM?
At 9:00 PM?
For
the Orion Nebula (M42), RA = 5.5 hr, Dec = -5.5 degrees
RA
=6 hr transits at midnight on Dec 21.
- =>
Orion transits at midnight on Dec 14.
Also
- Orion
transits at 3:00 a.m. on Oct. 31.
- Orion
transits at 9:00 p.m. on Jan 28.
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Example 1
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What
RA is on the meridian at a given date and time?
What
RA is on the meridian at 3:00 am on Feb. 21?
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Example 2
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what day does a given RA cross meridian at a specific time?
A
constellation is at RA = 14 hr. On what day will it cross
the meridian at 9:00 PM?
- When
14 hr crosses the meridian at 9:00 PM, 17 hr crosses the
meridian at midnight.
- On
Mar 21: 12 hr crosses the meridian at midnight.
- 17
- 12 = 5 hours
=>
2.5 months (10 weeks)
=> June 7
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More on
Finding
Objects
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- Circumpolar
objects can be visible any time of the year
- Example:
Polaris, the pole star.
- Southerly
objects are best observed during transit,
that is, when they cross the meridian.
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What's
up
Tonight?
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What's
"up" tonight?
- Go
to the A101/103 "Interesting
Astronomy Sites" list for links to what's happening
in the sky.
- Observing
suggestions
- Best
nights are when the Moon is absent.
- Get
away from city glare.
- Get
dark adapted (about > 20 minutes)
- Use
a "red light" to look at star charts/maps
so you keep your night vision
- Observing
suggestions
- Try
to pick out some "easy" constellations
such as the Big Dipper, the Little Dipper, Cygnus,
and Cassiopea.
- Planets
follow close to the ecliptic (the path of the sun
through the sky)
- Remember,
planets don't twinkle
- We
will discuss specific object to observe in class.
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Magnitudes
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- We
would like a way of specifying the relative brightness
of stars.
- Hipparchus
devised a the magnitude system 2100 years ago to classify
stars according to their apparent brightness.
- He
labeled 1080 stars as class 0, 1,.. 6.
- 0
was the brightest, 1 the next brightest, etc.
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Magnitude
Scale
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- The
magnitude scale is logarithmic.
- An
increase in magnitude by 2.5 means an object is a factor
of 10 dimmer, e.g.
- A
zero mag star is 10 times brighter than a 2.5 mag star.
- A
zero mag star is 100 times brighter than a 5 mag star.
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Logarithms
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Reminders
about Logarithms
The
table below list some sample base 10 logarithms.
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Logarithm
function
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Power
of 10
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log
(10) = 1
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101
= 10
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log
(1) = 0
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100
= 1
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log
(0.1) = -1
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10-1
= 0.1
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log
(2) = 0.3
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100.3
= 2
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log
(3) ~ 0.5
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100.5
~ 3
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log
(5) = 0.7
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100.7
= 5
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Note:
If we have z = 10x,
then x is the logarithm (base 10) of z. If z = ey
then y is the natural logarithm (base e, e = 2.71828)
of z. Base 10 logarithms are usually written as log10
or log, while nature logarithms are designated with ln.
Reminder:
We have 10x * 10y
= 10x+y. To multiply
(divide) two numbers, add (subtract) their logarithms
and take the anti-logarithm. In numerical terms, if
x = log(A) and y = log(B) then C = A*B can be determined
from C = 10x+y.
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Sample
Magnitudes
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The
apparent visual magnitude of some of the brightest objects
in the sky are given below.
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Object
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Apparent
Magnitude
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Sun
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-26.8
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Full
Moon
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-12.6
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Sirius
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-1.47
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Canopus
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-0.72
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Arcturus
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-0.06
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Betelgeuse
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0.41
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Magnitude
Limits
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| A
dark adapted person with good eyesight can see to ~6th magnitude.
Hubble
Space Telescope can observe objects at ~30 mag.
4x109
times fainter than the eye!
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Observing
at
Night
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Further
suggestions on sky gazing
- Go
to a dark spot, away from city lights
- Large
city has 3.5 mag limit.
- Country
has 5.5 mag limit.
- Mountains
have 6.5 mag limit.
- Get
dark adapted (worth repeating)
- This
can take up to 45 minutes.
- Use
a "red light" to look at star charts/maps
so you keep your night vision
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